Abstract This paper studies the revenue‐maximizing selling mechanism with a continuum of buyers who have two‐dimensional private information: valuation and entry cost. Using optimal control methods, we solve this two‐dimensional screening problem with endogenous entry and derive sufficient conditions under which the optimal mechanism is a posted price. These conditions reduce the original problem to a one‐dimensional one in which a buyer's type is net valuation, and the optimal posted price matches that of the transformed environment. Finally, under mild conditions, revenue maximization implies underselling relative to the efficient allocation.
Feng et al. (Tue,) studied this question.